Higher-order differentials of the period map and higher Kodaira-Spencer classes
| dc.creator | Karpishpan, Yakov | |
| dc.date | 1994-05-12 | |
| dc.date.accessioned | 2026-07-07T09:06:04Z | |
| dc.date.available | 2026-07-07T09:06:04Z | |
| dc.description | In \cite{K} we introduced two variants of higher-order differentials of the period map and showed how to compute them for a variation of Hodge structure that comes from a deformation of a compact Kähler manifold. More recently there appeared several works (\cite{BG}, \cite{EV}, \cite{R}) defining higher tangent spaces to the moduli and the corresponding higher Kodaira-Spencer classes of a deformation. The $n^{th}$ such class $κ_n$ captures all essential information about the deformation up to $n^{th}$ order. A well-known result of Griffiths states that the (first) differential of the period map depends only on the (first) Kodaira-Spencer class of the deformation. In this paper we show that the second differential of the Archimedean period map associated to a deformation is determined by $κ_2$ taken modulo the image of $κ_1$, whereas the second differential of the usual period map, as well as the second fundamental form of the VHS, depend only on $κ_1$ (Theorems 2, 5, and 6 in Section~3). Presumably, similar statements are valid in higher-order cases (see Section~4). | |
| dc.description | 18 pages, LaTeX | |
| dc.identifier | https://arxiv.org/abs/alg-geom/9405005 | |
| dc.identifier | http://arxiv.org/abs/alg-geom/9405005 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/149891 | |
| dc.subject | Algebraic Geometry | |
| dc.title | Higher-order differentials of the period map and higher Kodaira-Spencer classes | |
| dc.type | text |